Question
Asked Dec 2, 2019
1 views
Find f(x,y) and fy(x,y). Then, find fx (2, 3) and fy(-1,3)
2ху?
f(x,y)
e ху + 3
f(x.y)=
help_outline

Image Transcriptionclose

Find f(x,y) and fy(x,y). Then, find fx (2, 3) and fy(-1,3) 2ху? f(x,y) e ху + 3 f(x.y)=

fullscreen
check_circle

Expert Answer

Step 1

Given,

2хy?
f(x, y)
exy 3
and we need to compute f(x, y) and f,(x, y)
help_outline

Image Transcriptionclose

2хy? f(x, y) exy 3 and we need to compute f(x, y) and f,(x, y)

fullscreen
Step 2

For computing the partial derivative fx(x,y), we wil...

2ху?
дх (еху + 3
af (x, y)
fr(x, y)
дх
for a constant k
ckfx)(f())
a
X
= 2y2.
дх \еху + 3.
a(e*y3)
дх
(еху + 3)2
дх
(exy 3)
дх
Tusing quotient rule]
gf'-fg
= 2y2
g2
(е*У + 3) 1 — х (yе*У)
(exy 3)
[ekx)' ke*
= 2y2
2y2 (e*y3 xye*y)
(exy3)
f(x, y)
3 (2)-3)e2)(-3))
(e(2)(-3)3)2
2-3)2 (e(2)(-3)
fe(2,-3)
=
18(7e-63)
fr(2,-3)
(e-6+3)2
help_outline

Image Transcriptionclose

2ху? дх (еху + 3 af (x, y) fr(x, y) дх for a constant k ckfx)(f()) a X = 2y2. дх \еху + 3. a(e*y3) дх (еху + 3)2 дх (exy 3) дх Tusing quotient rule] gf'-fg = 2y2 g2 (е*У + 3) 1 — х (yе*У) (exy 3) [ekx)' ke* = 2y2 2y2 (e*y3 xye*y) (exy3) f(x, y) 3 (2)-3)e2)(-3)) (e(2)(-3)3)2 2-3)2 (e(2)(-3) fe(2,-3) = 18(7e-63) fr(2,-3) (e-6+3)2

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative